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Sides of a triangle are in the ratio of12:17:25 and its perimeter is 540cm. Find its area

    • Posted by Samrat Gundgal 5 years, 3 months ago

    CBSE > Class 09 > Mathematics
    • 2 answers

    Rudranshu Mishra 5 years, 3 months ago

    P=540cm. Sides=12x+17x+25x Perimeter=Sum of all sides. 540=54x x=10 Sides of triangle;120cm, 170cm, 250cm. Area of triangle =s√s(s-a) (s-b) (s-c) s=540÷2=270 s-a=270-120=150 s-b=270-170=100 s-c=270-250=20 √270×150×100×20 √81,000,000 9000cm²

    1Thank You

    Yogita Ingle 5 years, 3 months ago

    Ratio of the sides of the triangle = 12 : 17 : 25
    Let the common ratio be x then sides are 12x, 17x and 25x
    Perimeter of the triangle = 540cm
    12x + 17x + 25x = 540 cm
    ⇒ 54x = 540cm
    ⇒ x = 10
    Sides of triangle are,
    12x = 12 × 10 = 120cm
    17x = 17 × 10 = 170cm
    25x = 25 × 10 = 250cm
    Semi perimeter of triangle(s) = 540/2 = 270cm
    Using heron's formula,Area of the triangle = √s (s-a) (s-b) (s-c)                                       

    = √270(270 - 120) (270 - 170) (270 - 250)cm2                                       
    = √270 × 150 × 100 × 20 cm2                                       

    = 9000 cm2

    0Thank You

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